Lattice Refining LQC and the Matter Hamiltonian

Abstract

In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a non-self-adjoint Hamiltonian operator. Demanding that the solutions for the wave-functions obey certain physical restrictions, we impose constraints on the two-dimensional, $(A,\delta )$, parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.

15 pages, 3 figures, revtex style; amended version to match publication in Phys. Rev. D

References in corpus (8)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantization Ambiguities in Isotropic Quantum Geometry
• On the Hamiltonian Constraint of Loop Quantum Cosmology
• Lattice refining loop quantum cosmology, anisotropic models and stability
• On the regularization ambiguities in loop quantum gravity
• An algebraic extension of Dirac quantization: Examples
• Lattice Refining Loop Quantum Cosmology and Inflation
• Isotropic Loop Quantum Cosmology with Matter

Cited by in corpus (29)

• Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology
• Anomaly freedom in perturbative loop quantum gravity
• Introduction to Loop Quantum Cosmology
• Loop quantum gravity corrections to gravitational wave dispersion
• Is loop quantization in cosmology unique?
• Observational issues in loop quantum cosmology
• Consistent Loop Quantum Cosmology
• Generalized uncertainty principles and localization in discrete space
• Quantum nature of cosmological bounces
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• The gravitational wave background from super-inflation in Loop Quantum Cosmology
• Anomaly-free vector perturbations with holonomy corrections in loop quantum cosmology
• Harmonic cosmology: How much can we know about a universe before the big bang?
• Effective relational cosmological dynamics from Quantum Gravity
• Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology
• Unique factor ordering in the continuum limit of LQC
• The high-density regime of kinetic-dominated loop quantum cosmology
• Dirac Fields in Loop Quantum Gravity and Big Bang Nucleosynthesis
• Unstable Anisotropic Loop Quantum Cosmology
• Quintessence and (Anti-)Chaplygin Gas in Loop Quantum Cosmology
• Lattice refinement in loop quantum cosmology
• On the possibility of Dark Energy from corrections to the Wheeler-De Witt equation
• Fourth order deformed general relativity
• Lattice Refining Loop Quantum Cosmology from an Isotropic Embedding of Anisotropic Cosmology
• Classical versus quantum evolution for a universe with a positive cosmological constant
• Discretisation parameter and operator ordering in loop quantum cosmology with the cosmological constant
• A Momentous Arrow of Time
• The probability of inflation in Loop Quantum Cosmology
• Quantum gravity effects on space-time